Aims and Fit of Module

•	To introduce some commonly used mathematical structures.


•	To provide knowledge about basic results in arithmetic and group theory. 

 
•	To help with the transition from concrete to abstract mathematical thinking.


•	To present applications, such as data encryption, that rely heavily on abstract mathematics.


•	To demonstrate how algebraic structures can be used to unify diverse mathematical topics.


•	To develop the students’ skills in reading and writing mathematical proofs. 


•	To enrich the mathematical vocabulary of the students.

Learning outcomes

A	Apply the Euclidean Algorithm to integers or polynomials.

B	Work with fundamental mathematical concepts, such as relations and permutations.

C	Use modular arithmetic to solve problems related to cryptography and coding theory.

D	Recognise common algebraic structures, such as groups, rings or fields.

E	Find the image and kernel of a homomorphism and show (in simple cases) when two structures are isomorphic.

F	Apply basic results in group theory, such as Lagrange’s Theorem.

Method of teaching and learning

This module will be delivered by a combination of formal lectures and tutorials.